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arXiv · 1312.7415

On weighted $L^2$ estimates for solutions of the wave equation

Youngwoo Koh·Ihyeok Seo
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Abstract

In this paper we consider weighted $L^2$ integrability for solutions of the wave equation. For this, we obtain some weighed $L^2$ estimates for the solutions with weights in Morrey-Campanato classes. Our method is based on a combination of bilinear interpolation and localization argument which makes use of Littlewood-Paley theorem and a property of Hardy-Littlewood maximal functions. We also apply the estimates to the problem of well-posedness for wave equations with potentials.

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Youngwoo Koh, Ihyeok Seo. 2013-12-28. On weighted $L^2$ estimates for solutions of the wave equation. https://arxiv.org/abs/1312.7415

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